Some concepts that gave origin to classical mechanics are just too classical. We must have them here even if we came to suffer significantly to get rid of them when necessary. And the most basic of all classical concepts is the particle.
In classical mechanics, a particle is an eternal smallest element. It is a brick that builds everything that exists. Particles are the building blocks of any physical system. A particle has no size, no internal structure, but has some information attached. Typically, the information that comes with the particle is the mass, but it can also include other observables, as the electric charge, the spin, or additional internal charges. By eternal, we mean that a particle cannot be created or destroyed. A particle exists.
Of course, this concept of a particle does not have any real correspondence in nature. The real world has extended bodies, formed by molecules, atoms of many types, which are formed by electrons, protons, and neutrons. Protons and neutrons are then formed by other basic structures known as quarks. Electrons are elementary by themselves. However, quarks and electrons cannot be described as classical particles, because eventually, this concept will not be sufficient to specify the way they exist. To understand if we are found in the domain of classical physics, we should learn if the above concept of a particle is, at least, approximately accurate to experiment. If this is the case, we may address the electron as a classical particle. Sometimes the classical particle is a sufficient concept.
The set of information that comes with the particle depends on the specific physical system of interest. Mass is always one of the quantities, and it is related to the concept of inertia, which we will explore in moments. An electron, for example, has other defining quantities; the electric charge, and the spin. If we are treating an electron as a classical particle, these measures must be the defining properties of the electron. In this case, we have the values \(m_e\approx9,109\cdot10^{-31}\ Kg\), about \(1836\) times lighter than the proton, \(q_e\approx−1.602\cdot10^{−19}\ \text{coulomb}\), which is the elementary electric charge, and an intrinsic angular momentum, or spin, of \(1/2\). No other particle has the same characteristics, and all observers must agree with them.
The origin of mass, charge, and spin can only be explained by the relativistic quantum field theory. Therefore, in classical mechanics, these values must be postulated. But they are the first examples of what is called dynamical invariants. The values of \(\left(m_e,q_e,s_e\right)\) are always the same for the electron, as for any other particle, and they never change.
Another fundamental particle in nature is the photon, the particle of light and electromagnetic radiation. For centuries the debate about the nature of light opposed the particle and the wave points of view. Today, we understand the light fundamentally as a field, which can be made a particle when it reaches a detector. Still, it is also a wave when interacting with slits to form interference phenomena. The photon is of little use in classical mechanics since it has zero mass and zero electric charge. The photon does not have a spin value, but it has, on the other hand, a value called helicity, which gives rise to its polarization properties.